An inexact algorithm with proximal distances for variational inequalities

E. A. Papa Quiroz, L. Mallma Ramirez, P. R. Oliveira

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Abstract

In this paper we introduce an inexact proximal point algorithm using proximal distances for solving variational inequality problems when the mapping is pseudomonotone or quasimonotone. Under some natural assumptions we prove that the sequence generated by the algorithm is convergent for the pseudomonotone case and assuming an extra condition on the solution set we prove the convergence for the quasimonotone case. This approach unifies the results obtained by Auslender et al. [Math Oper. Res. 24 (1999) 644-688] and Brito et al. [J. Optim. Theory Appl. 154 (2012) 217-234] and extends the convergence properties for the class of φ-divergence distances and Bregman distances.

Original languageEnglish
Pages (from-to)159-176
Number of pages18
JournalRAIRO - Operations Research
Volume52
Issue number1
DOIs
StatePublished - 1 Jan 2018

Bibliographical note

Funding Information:
Acknowledgements. The first author’s research was supported by CAPES Project Graduate PAPD-FAPERJ Edital 2011. The second author was supported by CAPES and the third author was partially supported by CNPq.

Publisher Copyright:
© EDP Sciences, ROADEF, SMAI 2018.

Keywords

  • Proximal distance
  • Proximal point algorithm
  • Quasimonotone and pseudomonotone mapping
  • Variational inequalities

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